A Preliminary Mathematical Model for the Dynamic Transmission of Dengue, Chikungunya and Zika

Raúl Isea; Karl E. Lonngren

doi:7260178

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A Preliminary Mathematical Model for the Dynamic Transmission of Dengue, Chikungunya and Zika

Current Issue

Volume 3, 2016
Issue 2 (April)

Pages: 11-15 | Vol. 3, No. 2, April 2016 | Follow on

Paper in PDF Downloads: 392 Since Jun. 24, 2016 Views: 3931 Since Jun. 24, 2016

Authors

[1]

Raúl Isea, Institute of Advanced Studies – IDEA, Hoyo de la Puerta, Baruta, Venezuela.

[2]

Karl E. Lonngren, Department of Electrical and Computer Engineering, University of Iowa, Iowa City, Iowa, USA.

Abstract

Aedes aegypti is a known vector of Dengue, Chikungunya and Zika and the goal of this study is to propose the first mathematical model to describe the dynamic transmission of these three diseases. We present two preliminary models that consist of the SEIR model for the human populations and an SEI model for the vector to describe (a) the single transmission dynamics of dengue, Chikungunya or Zika, and (b) any possible coinfection between two diseases in the same population. In order to do that, we obtain an analytical solution of the system of 17 and 30 coupled differential equations for each model respectively, and later obtain the eigenvalues by analyzing the Jacobian matrix in order to begin the development of a surveillance system to prevent the spread of these three diseases.

Keywords

Epidemic, Differential Equation, Dengue, Chikungunya, Zika, Aedes aegypti

Reference

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Isea R and Lonngren KE. A Mathematical Model of Cancer Under Radiotherapy. International Journal of Public Health Research 2015; 3(6): 340-344.

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Isea R. Análisis matemático de la difusión de un rumor entre dos grupos de personas. Revista Electrónica Conocimiento Libre y Licenciamiento (CLIC) 2015; 8: 85-89.

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